## Introduction

The tabular outlines are the distillate of long-term studies in the analysis of the N.T. writings. It takes some time to become familiar with this presentation and all its implications. The following explanations may help.

## The tabular presentation in general

The outline of the single books is arranged in **two parallel tables**:

- On the left the author’s table of contents, on the right his stichometrical disposition.
- The two parts are carefully inter-related; they corroborate each other mutually.
- Priority, however, is given to the table of contents, the stichometry is just a recalculation.
- That means that the outline cannot be based on stichometrical observations,

but it can be confirmed this way.

The **different pages** may help to envisage the whole of the book concerned:

- In smaller writings, page 1 provides the complete outline with all paragraphs.
- In larger writings, the table on page 1 gives an overview that can be placed on a single page.
- On p. 2, eventually 3-4, brief explanations follow, also on the shaping of paragraphs and text.
- Thereafter in larger writings, a complete table follows, listing each individual paragraph.

## The table of contents

On the left, the sections are labeled according to the traditional and the systematic **segmentation**:

- far left: chapters and verses as in modern Bible editions, (irrelevant for the author’s disposition because introduced only in the 13th and 16th cent.);
- 2nd column: systematic structure with main parts, major parts, subsections and paragraphs;
- decimal numbering system: only one point after the main part (1st level), no point thereafter;
- zero parts: “0.” or “1.0” help to distinguish between short introductions and (main) parts.

The **caesuras** of the text are defined according to internal and formal signals:

- in narrative texts: at a scene change, i.e. a change of place, time and persons acting;
- in epistles/speeches: at a thematic change, a new address or another indication of a new thought.
- The parts of the same level should together constitute a unity, perhaps a concentric composition.

The **headlines** of the main parts / major parts / paragraphs should relate to each other, if possible:

- If first and last parts correspond to each other in some way, it is called a concentric composition.
- In a structure of five parts, the 2nd and 4th parts are often related, similarly in seven parts.
- Often the part in the center of a book or its sections contains also a central point in its contents.
- The subdivisions result in an uneven number of parts (3, 5 or 7) in almost all cases.
- According to Aristotle, freely adapted, a whole needs a middle.

## The stichometrical table, including the Fibonacci sequence

The columns on the left list the **results of counting stichoi** with regard to the respective passages:

- first, the number of lines in the
*Greek New Testament*(4th edition, 1993) for comparison; - then the number of
*stichoi*in the 15-syllables-standard (except Pastoral Epistles), in two forms:

at first rounded up, i.e. the last lines of a paragraph though incomplete are counted as full lines,

after that counted exactly, i.e. the remaining syllables of the last line are noted after the colon; - finally the number of paragraphs that are added up in the respective sum of
*stichoi*.

The columns on the right are distinguished according to numbers of the **Fibonacci sequence**:

- This is an old numerical sequence containing approximations to the golden ratio.
- It is named for the mathematician Leonardo of Pisa, (grand)son of Bonaccio (c. 1200).
- The sequence itself was already referred to by Nicomachus of Gerasa (2nd cent. AD).
- Each number of the sequence is the sum of the previous two: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 …
- The relation of two neighboring numbers is approximating the irrational value 0.6180339… :

see 2/3 = 0.666; 3/5 = 0.6; 5/8 = 0.625; 8/13 = 0.61538…; 13/21 = 0.61904…; 21/34 = 0.61764… - The square of one of these numbers differs by ±1 from the product of the two next two numbers:

e.g. 5x5 = 25; 3x8 = 24; 2x13 = 26; or 8x8 = 64; 5x13 = 65; 3x21 = 63 etc.

The **calculation of proportions** is made on the basis of six numbers of the Fibonacci sequence:

- In the larger books (1000 or more
*stichoi*) a modulus of 34*stichoi*seems to be applied;

since 3x34 = 102, the sum of*stichoi*is easy to calculate: 48x34 = 3x16x34 = 1632 (Mk). - In the smaller writings the modulus usually has a size of 21 or 13
*stichoi*. - Components of 8, 5, and 3
*stichoi*are also used for subdividing the main parts into paragraphs. - Paragraphs of 4 or 7 stichoi are relatively seldom; they are rendered by 8/2 and 8/2 + 3
*stichoi*. - Only in very few cases the calculated target of
*stichoi*is different from the result of the counting;

in these instances the target number of the last column is indicated by a different color.

## The explanations on pages 2 and following

The **explanations of the outline** give an overview of the composition as a whole:

- The table of contents summarizes the table of p. 1 as needed for the stichometrical comparisons.
- An additional line (shown in bold) seeks to formulate the theme of the whole writing.
- The following text demonstrates the principal idea of the composition in general and in detail.
- Deviating delimitations of the main parts are briefly discussed, if necessary.
- An important concern are the correspondences in terms of concentric compositions.

The **explanations of stichometry** recapitulate the results of the *stichoi* counting:

- The table of the main parts gives an overview of the stichometrical disposition.
- The
*stichoi*total of the whole book is expressed as the product out of a Fibonacci number. - Brief comments following describe some of the implications and consequences.
- Observations on the main parts are followed by those on the smaller parts of a book.

The **explanations of the paragraphing** refer to the *Greek New Testament* for comparison:

- The deviations are listed if a paragraph is transposed, deleted or newly inserted.
- No reasons are given for these changes; they result from careful reflections on caesuras.
- Changes of the place and number of paragraphs may increase or reduce the number of lines.
- Thus it is possible almost always to adjust the number of counted
*stichoi*to the calculated target.

The very few instances when a **16th syllable** is tolerated at the end of a paragraph are noted:

- In these cases it is not possible to decide whether the author miscounted unintentionally,
- whether he surpassed the standard of 15 syllables consciously (tolerant rules provided),
- or whether the original text contained less syllables and was lengthened only secondarily.
- At any rate, the
*stichoi*target is also realized by reducing the number of paragraphs.

The **explanations of the textual version** refer to deviations from the *Greek New Testament* as well:

- A textual variant is preferred over the
*GNT*text only in a few exceptional instances. - In almost all cases, the reason is a difference between the counted
*stichoi*and the*stichoi*target. - The text is shortened in most cases, very often by debated words, in square brackets in the
*GNT*. - The variations are always explained concisely by the usual criteria of textual criticism.
- The witnesses of the variants are briefly listed with the sigla of the Nestle-Aland
^{27}apparatus - Deviations from the punctuation of the
*GNT*are hardly ever noted or explained.

## Benefit for the interpretation

The stichometrical approach is helpful in uncovering the** author’s intention**:

- It is a way of trying to reconstruct the original disposition as intended by the author.
- It is often possible to show stichometrically where he brings out his main points,

esp. in concentric compositions or in the middle of a thematic unit. - Apparently the authors wanted to meet aesthetic standards: good news written in good form.
- The results have a certain objectivity because they can be verified mathematically.

This approach, however, implies some **assumptions** that are not undisputed among exegetes:

- The authors of the NT are trained rhetorically and know to write sophisticated texts.
- When disposing and writing down their texts they applied the
*stichos*as standard line. - They also applied the Fibonacci numbers (the use of which in literature can only be deduced).
- Every line is formulated and even calculated carefully; nothing is adopted thoughtlessly.
- Therefore the synchronic approach has priority over against the diachronic one.

The stichometrical approach will gain additional **plausibility** with every ancient writing in which number of lines and proportions have been clearly derived from Fibonacci numbers.

##
*More information*

- Schreiben nach Maß. Zur Stichometrie in der antiken Literatur (368 kB);
- Stichometry as a Useful Tool in Reconstructing the Original Dispositions. (9.6 MB)
- See also the literature to the single books.